Stream Function for 2-D Incompressible Source Flow Calculator

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Two-Dimensional Incompressible Flow

Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

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Elementary Flows

Flow and Lift Distribution

Flow over Airfoils and Wings

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✖Source Strength measures the magnitude or intensity of a source, which is a theoretical construct used to represent fluid flow emanating from a point.ⓘ Source Strength [Λ]			+10% -10%
✖Polar Angle is the angular position of a point from a reference direction.ⓘ Polar Angle [θ]			+10% -10%

✖The Source Stream Function is defined as the quantity of fluid moving across some convenient imaginary line for source flow.ⓘ Stream Function for 2-D Incompressible Source Flow [ψ_source]

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Formula

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Stream Function for 2-D Incompressible Source Flow

Formula

`"ψ"_{"source"} = "Λ"/(2*pi)*"θ"`

Example

`"14.92873m²/s"="134m²/s"/(2*pi)*"0.7rad"`

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Stream Function for 2-D Incompressible Source Flow Solution

STEP 0: Pre-Calculation Summary

Formula Used

Source Stream Function = Source Strength/(2*pi)*Polar Angle
ψ_source = Λ/(2*pi)*θ
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Source Stream Function - (Measured in Square Meter per Second) - The Source Stream Function is defined as the quantity of fluid moving across some convenient imaginary line for source flow.
Source Strength - (Measured in Square Meter per Second) - Source Strength measures the magnitude or intensity of a source, which is a theoretical construct used to represent fluid flow emanating from a point.
Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.

STEP 1: Convert Input(s) to Base Unit

Source Strength: 134 Square Meter per Second --> 134 Square Meter per Second No Conversion Required
Polar Angle: 0.7 Radian --> 0.7 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ_source = Λ/(2*pi)*θ --> 134/(2*pi)*0.7

Evaluating ... ...

ψ_source = 14.9287336620198

STEP 3: Convert Result to Output's Unit

14.9287336620198 Square Meter per Second --> No Conversion Required

FINAL ANSWER

14.9287336620198 ≈ 14.92873 Square Meter per Second <-- Source Stream Function

(Calculation completed in 00.004 seconds)

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Credits

Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

Shikha Maurya has created this Calculator and 100+ more calculators!

Verified by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

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< 7 Source Flow Calculators

Stream Function for Flow over Rankine Oval

Go Rankine Oval Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+(Source Strength/(2*pi))*(Polar Angle from Source-Polar Angle from Sink)

Stream Function for Semi-Infinite Body

Go Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+Source Strength/(2*pi)*Polar Angle

Velocity Potential for 2-D Source Flow

Go Velocity Potential = Source Strength/(2*pi)*ln(Radial Coordinate)

Radial Velocity for 2-D Incompressible Source Flow

Go Radial Velocity = (Source Strength)/(2*pi*Radial Coordinate)

Stream Function for 2-D Incompressible Source Flow

Go Source Stream Function = Source Strength/(2*pi)*Polar Angle

Source Strength for 2-D Incompressible Source Flow

Go Source Strength = 2*pi*Radial Coordinate*Radial Velocity

Stagnation Streamline Equation for Flow over Semi-Infinite Body

Go Stream Function = 0.5*Source Strength

Stream Function for 2-D Incompressible Source Flow Formula

Source Stream Function = Source Strength/(2*pi)*Polar Angle
ψ_source = Λ/(2*pi)*θ

What is the equation of streamline source flow?

The equation of streamline is a straight line of constant polar angle with the source at the origin.

What does stream function represents?

Stream function equal to constant gives the equation of a streamline and it is defined for two dimensional both rotational and irrotational flow.

How to Calculate Stream Function for 2-D Incompressible Source Flow?

Stream Function for 2-D Incompressible Source Flow calculator uses Source Stream Function = Source Strength/(2*pi)*Polar Angle to calculate the Source Stream Function, Stream Function for 2-D Incompressible Source Flow formula states that the function is directly proportional to the polar angle and the strength of the source, this implies that the streamlines, lines along which the stream function is constant, are radial lines emanating from the source point, with the density of streamlines increasing with strength of source. Source Stream Function is denoted by ψ_source symbol.

How to calculate Stream Function for 2-D Incompressible Source Flow using this online calculator? To use this online calculator for Stream Function for 2-D Incompressible Source Flow, enter Source Strength (Λ) & Polar Angle (θ) and hit the calculate button. Here is how the Stream Function for 2-D Incompressible Source Flow calculation can be explained with given input values -> 11.58648 = 134/(2*pi)*0.7.

FAQ

What is Stream Function for 2-D Incompressible Source Flow?

Stream Function for 2-D Incompressible Source Flow formula states that the function is directly proportional to the polar angle and the strength of the source, this implies that the streamlines, lines along which the stream function is constant, are radial lines emanating from the source point, with the density of streamlines increasing with strength of source and is represented as ψ_source = Λ/(2*pi)*θ or Source Stream Function = Source Strength/(2*pi)*Polar Angle. Source Strength measures the magnitude or intensity of a source, which is a theoretical construct used to represent fluid flow emanating from a point & Polar Angle is the angular position of a point from a reference direction.

How to calculate Stream Function for 2-D Incompressible Source Flow?

Stream Function for 2-D Incompressible Source Flow formula states that the function is directly proportional to the polar angle and the strength of the source, this implies that the streamlines, lines along which the stream function is constant, are radial lines emanating from the source point, with the density of streamlines increasing with strength of source is calculated using Source Stream Function = Source Strength/(2*pi)*Polar Angle. To calculate Stream Function for 2-D Incompressible Source Flow, you need Source Strength (Λ) & Polar Angle (θ). With our tool, you need to enter the respective value for Source Strength & Polar Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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